Like a cube, a rectangular prism also has six sides, but its opposite sides have the same area. So it has three sets of 2 faces each that have the same area.

Let us look at a rectangular prism below. ‘Opening up’ this rectangular prism will produce a net. A net is a flat diagram that contains the faces of a solid shape. The faces are arranged so that the diagram could be folded to form that solid (in this case, a rectangular prism). Drawing the net of a prism can help with calculating the surface area.

The surface area of a rectangular prism is the sum of the areas of the three sets of rectangular faces with the same area.

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

= (l x b x 2) + (b x h x 2) + (l x h x 2)

= 2(lb + bh + lh)

**Example 1**** :** Calculate the surface area of the rectangular prism here by first sketching a net diagram.

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

= (7 x 5 x 2) + (5 x 3 x 2) + (7 x 3 x 2)

= 70 + 30 + 42

= 142 cm^{2}

**Example 2**** :** For the rectangular prism shown here, sketch a net diagram, and then calculate the surface area.

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

= 2(14 x 11) + 2(11 x 8) + 2(14 x 8)

= 2 x 154 + 2 x 88 + 2 x 112

= 308 + 176 + 224

= 708 cm^{2}

**Example 3**** :** Calculate the surface area of a rectangular prism with dimensions: length = 80 mm, breadth = 45 mm, and height = 25 mm.

Surface area = 2 (lb + bh + lh)

= 2 (80 x 45 + 45 x 25 + 80 x 25)

= 2 (3600 + 1125 + 2000)

= 2 x 6725

= 13,450 mm^{2}

Here are some more examples of area of prisms.